Great question! Dr. Ken Rubin, a Professor in the Department of Geology at the University of Hawaii has a very clear explanation that walks through all of the evidence that allows us to figure out what is in the earth´s core. First, we know the overall density and mass of the Earth based on measurements of how the Earth perturbs the orbits of other planets and the moon.

Second, we know the overall density of the various layers of the Earth based upon the way in which seismic pressure waves (compressional waves created by earthquakes) move through the earth to arrive at locations remote from the earthquake source.

Third, by examining a second type of seismic wave (a shear wave, that is equivalent in motion to a back and forth rubbing of one's hands together) we know that the outer part of the core is liquid, even though it is at immense pressure from being underneath so much rock. Shear waves can't travel through liquids.

Forth, we know the overall composition of the Earth by examining the bulk chemical composition of the Sun (by examining its light spectrum) and by analyzing a class of meteorites known as Chondrites (which have similar composition to the Sun and are believed to be similar to the material from which the Earth accreted).

Fifth, we know the composition of the Earth's crust and its mantle, by examining samples of them. For the lower mantle, we use experiments of the effect of pressure on upper (shallow) mantle minerals to predict the mineralogy of the lower reaches of the mantle. We then pass seismic waves through it in the lab to see if our experimental rocks match the observations.

Six, now that we know the size, mass and composition of the whole Earth, its crust, and its mantle, we can construct a balance sheet of materials and see which chemical elements aren't in the crust (including atmosphere and hydrosphere) or mantle that we know should be on the Earth. These must be in the core.

Seven, to aid us in our assessment, we recall that we need metallic elements in high concentration somewhere in the interior of the Earth to generate our magnetic field. Also, this metal must be able to be in the liquid state even at very high pressures.

Adding all this up, we find the core is predominantly Iron metal (Fe). We find it has a significant amount of the element Nickel (Ni, about 4%) and a light element to make it less dense (about 10% by mass). This light element is either mostly oxygen or sulfur, with the arguments for oxygen (too detailed to go into here) being more believable in general.

We can look at the composition of iron meteorites as well, which are remnants of small planetary bodies from early in our solar-system's history that segregated small cores. The composition of these metal alloys match closely what we predict the composition of our core is using the evidence discussed above.

There are several answers on our database that can tell you about the evidence and experiments that show the core of the Earth is made of iron and nickel. You can read these answers here, or go to the links and read those answers from their original question:

1. The Earth's layers were discovered by looking at recordings of seismic waves generated by earthquakes. When an earthquake occurs, seismic waves travel throughout the earth. It is these seismic waves that cause the ground to shake near an earthquake. At great distances these waves can no longer be felt, but sensitive seismic instruments can still record them. Today's instruments are so sensitive that even moderate size earthquakes (magnitude 5) can be recorded on the other side of the world.

By looking at the recordings made by seismic instruments, scientists can figure out what the interior of the Earth looks like. This is much the same method as a CAT-scan used by doctors to image the brain.

The layers of the Earth were discovered during the first half of the 20th century after modern seismographs were invented. Scientists are still studying the details of the layers of the Earth in this way.

2. We can look at rocks on the surface and see that they are layered. We can also measure the larger-scale layers in the Earth by seeing the reflections and changes in direction that sound/earthquake waves make when hitting different layers in the Earth.

Earth´s inner core and outer core are both made of an iron-nickel alloy. The state of matter (solid, liquid or gas) of a given material depends on its temperature and pressure. Most materials, including iron and nickel, change from liquid to solid at lower temperatures and/or higher pressures. It´s easy to understand going from a solid to a liquid at higher temperatures because we are all familiar with ice melting on a warm day. Why do materials change from liquid to solid at higher pressure? For almost all materials (except water), atoms are packed closer together in the solid state than in the liquid state. So when you squeeze the atoms together with high pressure the material changes from liquid to solid.

As you go deeper in the Earth both temperature and pressure increases. Although the inner core is very hot, it is solid because it is experiencing very high pressure. The pressure in the outer core is not high enough to make it solid.